proposal: math/big: add Float.Pow, Float.Exp, Float.Ln?

[zboralski]

There is already an implementation in @robpike's excellent ivy calculator. However, the code is quite complex and lacks test cases.

Would it make sense to move it to the math/big package?

[ianlancetaylor]

Marking as 1.7 to make a decision--I have no opinion on what that decision should be.

[teknico]

I'll add computing Mandelbrot fractals with big.Float as motivation. Ideally a whole new big.Complex type, :-) or at least big.Float.Sqrt, and possibly big.Float.Exp too. See for instance exercise 3.8, page 63, of The Go Programming Language book:

"Rendering fractals at high zoom levels demands great arithmetic precision. Implement the same fractal using four different representations of numbers: complex64, complex128, big.Float, and big.Rat. How do they compare in performance and memory usage? At what zoom levels do rendering artifacts become visible?"

(Disregard big.Rat, it's way too slow for this kind of use anyway.)

Also, see this go-nuts discussion: math/big pow() and floor() help.

[griesemer]

@teknico Note that using complex numbers for Mandelbrot may make the implementation simpler, but it will also run a lot slower because there are a lot of shortcuts that are possible when dealing with the real and imaginary parts explicitly.

It does make sense to have Sqrt, and/or perhaps Exp instead.

We have been playing with implementations, but high-quality implementations that scale to arbitrary precision (ivy has an upper internal limit) are hard. We will get to it when we get to it.